One of the significant problems in digital signal processing is the filtering and reduction of undesired interference. Due to the abundance of methods and algorithms for processing signals characterized by complexity and effectiveness of removing noise from a signal, depending on the character and level of noise, it is difficult to choose the most effective method. So long as there is specific knowledge or grounds for certain assumptions as to the nature and form of the noise, it is possible to select the appropriate filtering method so as to ensure optimum quality. This chapter describes several methods for estimating the level of noise and presents a new method based on the properties of the smoothing filter.
TopIntroduction
The dynamic development of computer techniques that has been observed over the past twenty years and the development of digital algorithms for signal processing accompanying it allows for significant improvement of the quality of obtained images and purposeful interference in the image structure for bringing out certain qualities. Improvement of image quality makes it possible to obtain a significantly greater amount of useful information and also to create a better aesthetic impression.
Images documented as primary—model—are created, in principle, as a representation of the reality surrounding us in a form intelligible by the senses or are created as a creative manmade act. In the first case, representation is effected with the use of an available form of electromagnetic energy (radar, X-Ray apparatus, television camera, photographic camera), mechanical energy—ultrasound (ultrasound, echo sounding), or other forms of energy such as heat (thermal vision), or the energy of an electron beam (electron microscope).
It is clear that images obtained by means of technical devices as well as those that are purely manmade—especially those created using technical tools—are burdened with distortions. Distortions pertain to geometric changes of the obtained image relative to the model and also changes resulting from the superimposition of unnecessary information, constituting noise, onto the model image.
The causes of distortions are also to be sought in the interference of measuring energy in the observed environment and in imperfections of the apparatus (nonlinearity of processing, the influence of sampling, quantization, the limited band of signal transfer, limited by the capabilities of fixing the image on monitor screens or on paper). Distortions also appear as a result of the influence of external electromagnetic fields and other fields during processing and transmission of images.
A significant practical matter is the search for methods of improvement of image quality and removal of distortions being the effect of noise. The main tasks in this scope are tasks of searching for methods and algorithms of image analysis for:
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Removal of undesired noise from the image,
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Removal of specific image defects (e.g. geometrical),
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Improvement of images with low technical quality,
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Reconstruction of images that have been partially destroyed.
The computer technology used for achieving one of the above listed goals is called “digital image processing” technology. This technology is incomparable to other technologies (e.g. retouching in conventional photography) in terms of the achieved effects. In this technology, an image is defined as an NxM matrix with values in the range [0-255] corresponding to 28 distinct levels. A basic operation on a so-defined set of data, having the purpose of removing undesired qualities of the image or to influence its new properties, is the filtering of this data.
Effectiveness of filtering, expressed for example by the noise reduction coefficient, is a function of many factors including: (1) the selected filtering algorithm; (2) certain information with noise qualities; and (3) also certain information about the model image. Of special significance is information on the qualities of noise—random or determined, the distribution of power spectral density, variance, etc. In most cases, it is not possible to obtain full data on the noise and attempts at estimation are undertaken—assessment of the level of noise expressed by variance through analysis of image data. Using the information on the level of noise in the image allows for obtainment of an optimal filtering quality, especially for realization of problems of image reconstruction, edge detection, and others. It is also among the information necessary for the creation and operation of adaptive filtering algorithms.
The applications of noise level estimation in images are very wide and include, among others: